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At least 757 records · Page 42

Galileo to Jupiter: Probing the Planet and Mapping Its Moons

The first project to use the space shuttle as an interplanetary launch vehicle, the Galileo mission is designed to obtain information about the origin and evolution of the solar system by studying large-scale phenomena on Jupiter and its satellites. Aimed towards Mars to obtain gravity assist, the orbiting spacecraft will deploy a probe, which penetrating the Jovian atmosphere, will transmit data for approximately an hour. The spacecraft itself will inspect the atmospheres, ionospheres, and surfaces of Ganymede, Io, Europa, and Callisto, as well as determine their magnetic and gravitational properties. The experiments to be conducted and their scientific objectives are described. Known facts about the Jovian system are reviewed.

Source record↗

Design and test of a prototype thermal bus evaporator reservoir aboard the KC-135 0-g aircraft

The Thermal Bus Zero-G Reservoir Demonstration Experiment (RDE) has currently undergone two flights on the NASA-JSC KC-135 Reduced Gravity Aircraft. The objective of the experiment, which uses a smaller version of the evaporator reservoirs being designed for the Prototype Thermal Bus for Space Station, is to demonstrate proper 0-g operation of the reservoir in terms of fluid positioning, draining, and filling. The KC-135 was chosen to provide a cost-effective and timely evaluation of 0-g design issues that would be difficult to predict analytically. A total of fifty 0-g parabolas have been flown, each providing approximately 25-30 seconds of 0-g time. While problems have been encountered, the experiment has provided valuable design data on the 0-g operation of the reservoir. This paper documents the design of the experiment; the results of both flights, based on the high-speed movies taken during the flight and the visual observations of the experimenters; and the design modifications made as a result of the first flight and planned as a result of the second flight.

Brown, Richard F.↗

Characterizing and testing a thermally isolating superconducting link for SAFIRE-like missions

The discovery of a new class of ceramic superconductors with transition temperatures above the boiling point of liquid nitrogen has opened the doors for several space applications. One important space application is the fabrication of an electrically conducting and thermally isolating link to replace manganin wires used in connecting IR detectors to data acquisition electronics on remote sensing platforms like SAFIRE and SIRTF. These NASA platforms designed to monitor the earth's atmosphere from space use infrared detectors which operate at liquid helium temperature (4.2K) for optimum performance. The SAFIRE mission employs hybrid dewars which combine both mechanical and cryogenic liquid cooling. The lifetime of such a mission is limited by the heat conducted through sensor array leads that connect the electronics (at approximately 80 K) to the sensors (at approximately 4 K). Currently these remoter sensing systems use manganin wires to connect the IR detectors to the data acquisition electronics. This link between a detector operating at 4 K and electronics operating at 80 K must be made of material that has high electrical conductivity and high thermal resistance. The YBCO superconductor with a transition temperature, Tc, of 93 K can achieve these conflicting requirements. A link with these characteristics will improve the thermal isolation of IR detectors and will increase the lifetime of the cryogen. The fabrication of an electrically conducting and thermally isolating link that replaces the manganin wires is an important application that will improve thermal isolation of IR detectors and will increase the lifetime of the cryogen. The link is made by screen printing superconducting lines on a low thermal conductivity ceramic substrate. Developing, modeling, and testing this high temperature superconducting link is a collaborative effort among NASA-Langley Research Center, Christopher Newport University (CNU), Clemson University and the industrial companies that have joined the Commercialization of Space Program for the purpose of developing and testing this link. CNU's effort in the development of this superconducting link included the following major efforts: (1) Development of a thermal conductivity measurement system for high temperature superconductors and ceramic materials which are potential candidates for use as substrates in this link. (2) Development of a mathematical model for the superconducting link that studies the effect of materials and geometry on the heat load and life time of missions. (3) Characterization of high Tc materials and assemblies made for space applications. Properties studied include humidity effects and aging effects on high Tc materials. This report summarizes the results of the research studies that were completed. Copies of publications detailing these findings are attached to this report.

Selim, Raouf R.↗

Optimal carbon storage reservoir management through deep reinforcement learning

Model-based optimization plays a central role in energy system design and management. The complexity and high-dimensionality of many process-level models, especially those used for geosystem energy exploration and utilization, often lead to formidable computational costs when the dimension of decision space is also large. This work adopts elements of recently advanced deep learning techniques to solve a sequential decision-making problem in applied geosystem management. Specifically, a deep reinforcement learning framework was formed for optimal multiperiod planning, in which a deep Q-learning network (DQN) agent was trained to maximize rewards by learning from high-dimensional inputs and from exploitation of its past experiences. To expedite computation, deep multitask learning was used to approximate high-dimensional, multistate transition functions. Both DQN and deep multitask learning are pattern based. As a demonstration, the framework was applied to optimal carbon sequestration reservoir planning using two different types of management strategies: monitoring only and brine extraction. Both strategies are designed to mitigate potential risks due to pressure buildup. Results show that the DQN agent can identify the optimal policies to maximize the reward for given risk and cost constraints. Finally, experiments also show that knowledge the agent gained from interacting with one environment is largely preserved when deploying the same agent in other similar environments.

15 GEOTHERMAL ENERGY↗

Program to design, fabricate, test, and deliver a thermal control-mixing control device for the George C. Marshall Space Flight Center

The development and testing of a temperature sensor and pulse duration modulation (PDM) diverter valve for a thermal control-mixing control device are described. The temperature sensor selected for use uses a fluidic pin amplifier in conjunction with an expansion device. This device can sense changes of less than 0.25 F with greater than 15:1 signal to noise ratio when operating with a typical Freon pump supplied pressure. The pressure sensitivity of the sensor is approximately 0.0019 F/kPa. The valve which was selected was tested and performed with 100% flow diversion. In addition, the valve operates with a flow efficiency of at least 95%, with the possibility of attaining 100% if the vent flow of the PDM can be channeled through the last stage of the diverter valve. A temperature sensor which utilized an orifice bridge circuit and proportional-vortex combination mixing valve were also evaluated, but the concepts were rejected due to various problems.

Thurston, T. S.↗

Fast Neutron Spectrum Potassium Worth for Space Power Reactor Design Validation

A variety of critical experiments were constructed of enriched uranium metal (oralloy ) during the 1960s and 1970s at the Oak Ridge Critical Experiments Facility (ORCEF) in support of criticality safety operations at the Y-12 Plant. The purposes of these experiments included the evaluation of storage, casting, and handling limits for the Y-12 Plant and providing data for verification of calculation methods and cross-sections for nuclear criticality safety applications. These included solid cylinders of various diameters, annuli of various inner and outer diameters, two and three interacting cylinders of various diameters, and graphite and polyethylene reflected cylinders and annuli. Of the hundreds of delayed critical experiments, one was performed that consisted of uranium metal annuli surrounding a potassium-filled, stainless steel can. The outer diameter of the annuli was approximately 13 inches (33.02 cm) with an inner diameter of 7 inches (17.78 cm). The diameter of the stainless steel can was 7 inches (17.78 cm). The critical height of the configurations was approximately 5.6 inches (14.224 cm). The uranium annulus consisted of multiple stacked rings, each with radial thicknesses of 1 inch (2.54 cm) and varying heights. A companion measurement was performed using empty stainless steel cans; the primary purpose of these experiments was to test the fast neutron cross sections of potassium as it was a candidate for coolant in some early space power reactor designs.The experimental measurements were performed on July 11, 1963, by J. T. Mihalczo and M. S. Wyatt with additional information in its corresponding logbook. Unreflected and unmoderated experiments with the same set of highly enriched uranium metal parts were performed at the Oak Ridge Critical Experiments Facility in the 1960s and are evaluated in the International Handbook for Evaluated Criticality Safety Benchmark Experiments (ICSBEP Handbook) with the identifier HEU MET FAST 051. Thin graphite reflected (2 inches or less) experiments also using the same set of highly enriched uranium metal parts are evaluated in HEU MET FAST 071. Polyethylene-reflected configurations are evaluated in HEU-MET-FAST-076. A stack of highly enriched metal discs with a thick beryllium top reflector is evaluated in HEU-MET-FAST-069, and two additional highly enriched uranium annuli with beryllium cores are evaluated in HEU-MET-FAST-059. Both detailed and simplified model specifications are provided in this evaluation. Both of these fast neutron spectra assemblies were determined to be acceptable benchmark experiments. The calculated eigenvalues for both the detailed and the simple benchmark models are within ~0.26 % of the benchmark values for Configuration 1 (calculations performed using MCNP6 with ENDF/B-VII.1 neutron cross section data), but under-calculate the benchmark values by ~7s because the uncertainty in the benchmark is very small: ~0.0004 (1s); for Configuration 2, the under-calculation is ~0.31 % and ~8s. Comparison of detailed and simple model calculations for the potassium worth measurement and potassium mass coefficient yield results approximately 70 – 80 % lower (~6s to 10s) than the benchmark values for the various nuclear data libraries utilized. Both the potassium worth and mass coefficient are also deemed to be acceptable benchmark experiment measurements.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Electrical enclosure hydrogen intrusion study

As a cost savings measure for the space shuttle program, the feasibility of substituting dry air for nitrogen as the purge gas used to minimize the probability of fire and explosions which could erupt from propellant vapor (hydrogen) diffusion into the electrical enclosures at Launch Complex 39 was investigated. It was concluded that: (1) Hydrogen concentrations of approximately 1% were obtained in an electrical enclosure under design purge conditions. (2) Hydrogen concentrations exceeding the lower explosive limit, 4%, could probably be obtained within the enclosure under worst case conditions. (3) Most of the hydrogen intrusion into the enclosure probably occurred at the point with the shortest leak path, such as the door seal. (4) More stringent electrical enclosure design requirements should be imposed before air is using as a purge gas.

Welch, P. J.↗

High-speed spatial scanning pyrometer

A high-speed spatial scanning pyrometer has been designed and developed to measure spectral radiance temperatures at multiple target points along the length of a rapidly heating/cooling specimen in dynamic thermophysical experiments at high temperatures (above about 1800 K). The design, which is based on a self-scanning linear silicon array containing 1024 elements, enables the pyrometer to measure spectral radiance temperatures (nominally at 650 nm) at 1024 equally spaced points along a 25-mm target length. The elements of the array are sampled consecutively every 1 microsec, thereby permitting one cycle of measurements to be completed in approximately 1 msec. Procedures for calibration and temperature measurement as well as the characteristics and performance of the pyrometer are described. The details of sources and estimated magnitudes of possible errors are given. An example of measurements of radiance temperatures along the length of a tungsten rod, during its cooling following rapid resistive pulse heating, is presented.

Cezairliyan, A.↗

Space Technology 5: Enabling Future Micro-Sat Constellation Science Missions

The Space Technology 5 (ST-5) Project is part of NASA s New Millennium Program. ST-5 will consist of a constellation of three micro-satellites, each approximately 25 kg in mass. The mission goals are to demonstrate the research-quality science capability of the ST-5 spacecraft; to operate the three spacecraft as a constellation; and to design, develop and flight-validate three capable micro-satellites with new technologies. ST-5 is designed to measurably raise the utility of small satellites by providing high functionality in a low mass, low power, and low volume package. The whole of ST-5 is greater than the sum of its parts: the collection of components into the ST-5 spacecraft allows it to perform the functionality of a larger scientific spacecraft on a micro-satellite platform. The ST-5 mission was originally designed to be launched as a secondary payload into a Geosynchronous Transfer Orbit (GTO). Recently, the mission has been replanned for a Pegasus XL dedicated launch into an elliptical polar orbit. A three-month flight demonstration phase, beginning in March 2006, will validate the ability to perform science measurements, as well as the technologies and constellation operations. ST- 5 s technologies and concepts will then be transferred to future micro-sat science missions.

Carlisle, Candace C.↗

Space Technology 5: Enabling Future Micro-Sat Constellation Science Missions

The Space Technology 5 (ST-5) Project is part of NASA s New Millennium Program. ST-5 will consist of a constellation of three micro-satellites, each approximately 25 kg in mass. The mission goals are to demonstrate the research-quality science capability of the ST-5 spacecraft, to operate the three spacecraft as a constellation; and to design, develop and flight-validate three capable micro-satellites with new technologies. ST-5 is designed to measurably raise the utility of small satellites by providing high functionality in a low mass, low power, and low volume package. The whole of ST-5 is greater than the sum of its parts: the collection of components into the ST-5 spacecraft allows it to perform the functionality of a larger scientific spacecraft on a micro-satellite platform. The ST-5 mission was originally designed to be launched as a secondary payload into a Geosynchronous Transfer Orbit (GTO). Recently, the mission has been replanned for a Pegasus XL dedicated launch into an elliptical polar orbit. A three-month flight demonstration phase, beginning in March 2006, will validate the ability to perform science measurements, as well as the technologies and constellation operations. ST- 5 s technologies and concepts will then be transferred to future micro-sat science missions.

Carlisle, Candace C.↗

Space Communications Emulation Facility

Establishing space communication between ground facilities and other satellites is a painstaking task that requires many precise calculations dealing with relay time, atmospheric conditions, and satellite positions, to name a few. The Space Communications Emulation Facility (SCEF) team here at NASA is developing a facility that will approximately emulate the conditions in space that impact space communication. The emulation facility is comprised of a 32 node distributed cluster of computers; each node representing a satellite or ground station. The objective of the satellites is to observe the topography of the Earth (water, vegetation, land, and ice) and relay this information back to the ground stations. Software originally designed by the University of Kansas, labeled the Emulation Manager, controls the interaction of the satellites and ground stations, as well as handling the recording of data. The Emulation Manager is installed on a Linux Operating System, employing both Java and C++ programming codes. The emulation scenarios are written in extensible Markup Language, XML. XML documents are designed to store, carry, and exchange data. With XML documents data can be exchanged between incompatible systems, which makes it ideal for this project because Linux, MAC and Windows Operating Systems are all used. Unfortunately, XML documents cannot display data like HTML documents. Therefore, the SCEF team uses XML Schema Definition (XSD) or just schema to describe the structure of an XML document. Schemas are very important because they have the capability to validate the correctness of data, define restrictions on data, define data formats, and convert data between different data types, among other things. At this time, in order for the Emulation Manager to open and run an XML emulation scenario file, the user must first establish a link between the schema file and the directory under which the XML scenario files are saved. This procedure takes place on the command line on the Linux Operating System. Once this link has been established the Emulation manager validates all the XML files in that directory against the schema file, before the actual scenario is run. Using some very sophisticated commercial software called the Satellite Tool Kit (STK) installed on the Linux box, the Emulation Manager is able to display the data and graphics generated by the execution of a XML emulation scenario file. The Emulation Manager software is written in JAVA programming code. Since the SCEF project is in the developmental stage, the source code for this type of software is being modified to better fit the requirements of the SCEF project. Some parameters for the emulation are hard coded, set at fixed values. Members of the SCEF team are altering the code to allow the user to choose the values of these hard coded parameters by inserting a toolbar onto the preexisting GUI.

Hill, Chante A.↗

A Holistic Approach for Risk Management During Design

In this paper, an approach for the identification, assessment, mitigation and continuous management of risks during the process of designing a space mission is presented. This approach has been developed by observing the risk patterns that occur at the Project Design Center of the Jet Propulsion Laboratory (TeamX) which develops conceptual, concurrent design of Space Missions. TeamX develops an end-to-end conceptual design of a Space Mission in a matter of one or two weeks. As the risk chair in TeamX, the author has had the opportunity to observe the risk patterns that occur during design over the course of many design sessions. This paper introduces an abstraction and generalization of those patterns. Risk is defined as anything that can go wrong, along with its approximate likelihood and consequence. The indicators, and causes, and effects of these risks are cross cutting across the multiple levels of people and processes involved in the design, and the actual design product itself.

reliability analysis↗

Fuzzy Modeling and Parallel Distributed Compensation for Aircraft Flight Control from Simulated Flight Data

A method is described that combines fuzzy system identification techniques with Parallel Distributed Compensation (PDC) to develop nonlinear control methods for aircraft using minimal a priori knowledge, as part of NASA’s Learn-to-Fly initiative. A fuzzy model was generated with simulated flight data, and consisted of a weighted average of multiple linear time invariant state-space cells having parameters estimated using the equation-error approach and a least-squares estimator. A compensator was designed for each subsystem using Linear Matrix Inequalities (LMI) to guarantee closed-loop stability and performance requirements. This approach is demonstrated using simulated flight data to automatically develop a fuzzy model and design control laws for a simplified longitudinal approximation of the F-16 nonlinear flight dynamics simulation. Results include a comparison of flight data with the estimated fuzzy models and simulations that illustrate the feasibility and utility of the combined fuzzy modeling and control approach.

Weinstein, Rose↗

Launch Complex 39B, SWMU 009 Air Sparging System Expansion Implementation Work Plan Kennedy Space Center, Florida

This Implementation Work Plan (IWP) for expansion of the Air Sparging (AS) system at Launch Complex 39B (LC39B), presents the design and coordination specifics to expand the existing AS Interim Measure (IM) at LC39B located at Kennedy Space Center (KSC), Florida. The existing AS system at LC39B was installed in 2017 and included 279 AS wells. LC39B has been designated as Solid Waste Management Unit (SWMU) 009 under the KSC Resource Conservation and Recovery Act (RCRA) Corrective Action Program. Expansion of the AS IM will include installation of an additional five AS wells to depths of approximately 13 and 17 feet below land surface (bls) to remediate contaminated groundwater identified northwest of the launch pad, near the liquid oxygen (LOX) tank. The expansion will target concentrations of cis-1,2-dichloroethene (cDCE) and vinyl chloride (VC) greater than Florida Department of Environmental Protection (FDEP) Natural Attenuation Default Concentrations (NADCs) that were identified during direct push technology (DPT) sampling events between 2019-2022 in shallow intervals between 8 and 16 feet bls. The objective for this expansion is to remediate contaminated groundwater within the treatment zone to below NADCs to support transition to monitored natural attenuation (MNA) through a long-term monitoring (LTM) program. This expansion will treat approximately 0.07-acres of residual groundwater contamination. The IWP design for this expansion will utilize the existing AS system trailer that is already onsite and operating. The five new AS expansion wells will be integrated into the existing Zone Z4 distribution manifold to deliver compressed air to the new AS wells. To deliver airflow, three existing lateral lines will be split in the field at a lateral split junction point (using 2-way or 3-way splits). Each split lateral will supply air to AS wells at the same depth interval to minimize preferential pathways. The trenching layout for the new AS wells was developed to minimize ground disturbance due to the amount of utilities in the area. One new monitoring well will also be installed and added to LC39B’s performance monitoring program to evaluate the effectiveness of the AS system expansion. This well will be sampled on a semi-annual basis for volatile organic compounds, with results evaluated to determine if system adjustments may be required. The main components of this IWP were presented to the KSC Remediation Team (KSCRT) at the October 2022 Meeting (Meeting 2210-M05). DPT delineation data from the LOX area were also presented, which included some inferred boundaries due to physical restrictions of the LOX tank and associated concrete pad and infrastructure. Planned monitoring well sampling in this area will help determine if back-diffusion may be occurring from beneath the pad. Additionally, based on potential petroleum odors and staining identified at two DPT locations during the January 2022 DPT event in the 10-16 feet bls range, a KSCRT action item was assigned during the October 2022 meeting to collect soil samples for petroleum compounds if similar odors or staining are identified during IM implementation. Construction completion and performance monitoring will be incorporated into LC39B’s groundwater monitoring reports, which are currently submitted on an annual basis to FDEP to document operation and maintenance activities and results from the AS IM.

Deborah M. Wilson↗

The ISO SWS on-line system

The software which is currently being developed for the Short Wavelength Spectrometer (SWS) of the Infrared Space Observatory (ISO) is described. The spectrometer has a wide range of capabilities in the 2-45 micron infrared band. SWS contains two independent gratings, one for the long and one for the short wavelength section of the band. With the gratings a spectral resolution of approximately 1000 to approximately 2500 can be obtained. The instrument also contains two Fabry-Perault's yielding a resolution between approximately 1000 and approximately 20000. Software is currently being developed for the acquisition, calibration, and analysis of SWS data. The software is firstly required to run in a pipeline mode without human interaction, to process data as they are received from the telescope. However, both for testing and calibration of the instrument as well as for evaluation of the planned operating procedures the software should also be suitable for interactive use. Thirdly the same software will be used for long term characterization of the instrument. The software must work properly within the environment designed by the European Space Agency (ESA) for the spacecraft operations. As a result strict constraints are put on I/O devices, throughput etc.

Roelfsema, P. R.↗

Interval Management Display Design Study

In 2012, the Federal Aviation Administration (FAA) estimated that U.S. commercial air carriers moved 736.7 million passengers over 822.3 billion revenue-passenger miles. The FAA also forecasts, in that same report, an average annual increase in passenger traffic of 2.2 percent per year for the next 20 years, which approximates to one-and-a-half times the number of today's aircraft operations and passengers by the year 2033. If airspace capacity and throughput remain unchanged, then flight delays will increase, particularly at those airports already operating near or at capacity. Therefore it is critical to create new and improved technologies, communications, and procedures to be used by air traffic controllers and pilots. National Aeronautics and Space Administration (NASA), the FAA, and the aviation industry are working together to improve the efficiency of the National Airspace System and the cost to operate in it in several ways, one of which is through the creation of the Next Generation Air Transportation System (NextGen). NextGen is intended to provide airspace users with more precise information about traffic, routing, and weather, as well as improve the control mechanisms within the air traffic system. NASA's Air Traffic Management Technology Demonstration-1 (ATD-1) Project is designed to contribute to the goals of NextGen, and accomplishes this by integrating three NASA technologies to enable fuel-efficient arrival operations into high-density airports. The three NASA technologies and procedures combined in the ATD-1 concept are advanced arrival scheduling, controller decision support tools, and aircraft avionics to enable multiple time deconflicted and fuel efficient arrival streams in high-density terminal airspace.

Baxley, Brian T.↗

Measuring the Wear and Abrasive Resistance of Air Plasma Sprayed Aluminum Oxide for Lunar Exploration

Lunar regolith, especially finer dust particles traveling at high velocities, can cause significant wear and abrasive damage to structural components that ensure a prolongated presence on the surface of the Moon. With the absence of an atmosphere and lower gravity than on Earth, regolith particles maintain high velocities at large distances from where they were generated, for example next to lunar landers. Wear-resistant ceramic and ceramic composite materials can improve the durability of spacecraft components during long missions on the Moon’s surface. Aluminum oxide coatings are lightweight, have multifunctional properties, and have high strength including high hardness and wear resistance. These properties can help improve the durability of structures used in space exploration. Air plasma sprayed (APS) aluminum oxide coatings have demonstrated the potential to protect critical structures. This study investigated the abrasive wear resistance of APS aluminum oxide coatings via Taber abrasion experiments. Taber abrasion offers the advantage of quantifying the abrasive wear behavior of particles with different shapes on a surface. In this work, an abrasive wheel made of silicon carbide was utilized to evaluate wear properties of specimens progressively over 5000 cycles. This experiment focused on testing two series of specimens to determine whether a bond coat composed of nickel, chromium, aluminum, and yttrium (NiCrAlY) improved the protective behavior of the APS aluminum oxide coating. The specimens varied in topcoat thickness and were made with and without an approximately 100 µm bond coat layer. The mass of the specimens was measured at 400 cycles, 800 cycles, 3800 cycles, and 5000 cycles. Increasing thickness was found to result in higher wear for samples with and without a bond coat. Increased mass loss in samples with a bond coat was observed indicating a need for further studies on the overall impact of the use of a bond coat on the protective behavior of the coatings. To continue designing wear resistant coatings for structural protection in space missions, the multifunctional properties of the APS aluminum oxide coating will be studied. Future experiments will determine whether the APS aluminum oxide coating can protect the structures from other aspects of the harsh space environment, such as extreme temperature variations and ionizing radiation.

aluminum oxide↗

Variational Bayesian strategies for high-dimensional, stochastic design problems

This paper is concerned with a lesser-studied problem in the context of model-based, uncertainty quantification (UQ), that of optimization/design/control under uncertainty. The solution of such problems is hindered not only by the usual difficulties encountered in UQ tasks (e.g. the high computational cost of each forward simulation, the large number of random variables) but also by the need to solve a nonlinear optimization problem involving large numbers of design variables and potentially constraints. We propose a framework that is suitable for a class of such problems and is based on the idea of recasting them as probabilistic inference tasks. To that end, we propose a Variational Bayesian (VB) formulation and an iterative VB–Expectation-Maximization scheme that is capable of identifying a local maximum as well as a low-dimensional set of directions in the design space, along which, the objective exhibits the largest sensitivity. We demonstrate the validity of the proposed approach in the context of two numerical examples involving thousands of random and design variables. In all cases considered the cost of the computations in terms of calls to the forward model was of the order of 100 or less. The accuracy of the approximations provided is assessed by information-theoretic metrics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗